Not on a circle, but on a spiral

Cosmic bodies may have different shape of orbit: 8-shape, elongated and circular. This article considered only the movement on orbits almost the circular. The planets and some their satellites rotating, usually, on such orbits.

About spiral movement of celestial bodies it was known since the most ancient times. For example, the ancient Greek philosopher Plato wrote in the dialogue Timaeus: ”... Movement identical informs for all star circles spiral bending due to the opposing aspirations of two [major movements]”. Under the opposite aspiration of two [major movements] here be understood counteraction of force of gravity and centrifugal force (now these concepts are challenged, them gives other names, but as them do not name, the essence from it does not change)

In an ideal case, when these two forces are equal, the vector of speed of a rotating body is directed on a tangent to an orbit, perpendicularly radius. However, in the actual world, it is difficult to find something ideal. The predominance of one force, over another leads to a deviation of a vector of speed aside greater force and to rotation on a spiral.

If force of gravitation prevails, the vector of speed deviates to the center of rotation, and movement goes on a descending spiral. If centrifugal force prevails, movement goes on an ascending spiral. The last satellite can 'come off ' from the star, if force of gravitation significantly will weaken. So in cosmos appears free moons. The satellite, nearest to the center, rotates on a descending spiral, because of predominance of force of gravitation. Ultimately, it can lead to falling of the satellite on the central body. Both these forces are not constant and tend to equilibrium.

If the orbit has removing, the speed will be decreasing and, consequently, centrifugal force will be decreasing too. That is, the centrifugal force as though would, adjusts to the changing force of gravity. Although these two forces are not equal, they can be regarded as relatively equal at this point of time Fc=-Fg.

In the simplified version centrifugal force is defined under the formula:

Fc=-mp*v2/R,  mp – mass of planet, v – speed of planet, R - radius of rotation.

Force of gravity is defined under the law of universal gravitation of Newton::

Fg = G*ms*mp/ R2, где ms и mp – mass of the Sun and planet, R2 - square of the distance between them, G - gravitational constant. ~6.67384*10-11м³/(кg/с²).

Let's record equality of two forces:

G*ms*mp/ R2=- mp*v2 / R

Let's will simplify expression. Both sides of the equality will multiply at R and will divide at Mp and will get:

G*ms/ R=-v2

It follows, that the less mass of the Sun and more distance from him, the slower the movement of planets in orbit. Conversely, the greater the mass of the Sun and the smaller radius, the greater the speed. This is confirmed by modern calculations and measurements of the speed of the planets (see table 1).

With change of the orbit, speed of a celestial body in orbit is changed too. This was known also to ancient greek astronomers: «... One of its has rotating a greater circle, others smaller. Besides, on smaller circles they went more quickly, but on greater circles – more slowly » (Platon, dialogue Timaeus). At decrease of orbit, speed of celestial body is increasing and centrifugal force increases.

Dynamics of orbits

According to the law of universal gravitation of Newton, force of gravity inversely proportional to a square of radius, i.e. decreases in process of removal and, to the contrary, increases as approaching the central body. Table 1 sets out the main characteristics of the planets of the solar system (hereinafter the SS). The asteroid belt (destroyed planet) in the table represents, its moon, Ceres, preserved whole. Two dwarf planets: Pluto and Haumea represents the Kuiper belt, because for other objects are not enough information.

Table. 1 The main planets of Sun system

 № ~Mass kg Density (kg/m3) Equatorial radius  (km) (m) Average orbital speed  (m/s) The planets with a hard shell (without rings) 1 0,33022×1024 5427 2440 0,57909*1011 58,65d 4,7362*104 - 2 4,8676×1024 5243 6052 1,08208*1011 243,16d 3,502*104 - 3 5,97219×1024 5515 6378 1,49598*1011 23h.56m 2,978*104 1 4 0,64185×1024 3933 3393 2,27939*1011 24h.37m 2,4077*104 2 The planets - gas spheres (have rings) 5 3.6*1021 суммарная масса 9,43*1020 2077 От 0.3 до 950 487,3 299-494   4,13767*1011 20.0   1,7882*104 1 6 1898,6×1024 1326 71492 7,785472*1011 9h.50m 1,307*104 62 7 568,46×1024 687 60268 14,334494*1011 10h.14m 0,969*104 34 8 86,81×1024 1270 25559 28,766791*1011 10h.42m 0,681*104 27 9 102,43×1024 1638 24264 45,034437*1011 16чh 0,543*104 13 Kuiper belt 10 1,305·1022 2030 1153 59,06462*1011 6,39d 0,4666*104 5 11 0,4006*1022 2600?? 718 64,30544*1011 3,9h 0,4484*104 2

* The data for the table 1 are taken from Wikipedia on the date of 07.07.2014 and may not match of further changes. Due to frequent changes, the values cause no confidence in their accuracy.

On the basis of data from table 1, it is possible to calculate approximate values of force of gravity and centrifugal force and their ratio, on the basis of the formulas resulted above.

The results of calculation of the force of gravity and the centrifugal force for the 11 planets are shown in table 2, in order of their distance from the Sun. For all planets they are not equal. Consequently, they all have a spiral orbit.

Table 2. Difference between gravity and centrifugal forces
 Mercury Venus Earth Mars Ceres (moon) Jupiter Saturn Uranus Neptune Pluto Haumea Fg n 13,072 *1021 55,186 *1021 35,425 *1021 1,6399 *1021 0,07312 *1019 415,811 *1021 36,725 *1021 1,393 *1021 0,6705 *1021 0,005*1019 0,0013*1019 Fc n 12,791 *1021 55,168 *1021 35,404 *1021 1,6324 *1021 0,07288 *1019 416,581 *1021 37,236 *1021 1,399 *1021 0,6706 *1021 0,0048*1019 0,00125*1019 Fg-Fc 0,281 *1021 0,018 *1021 0,021 *1021 0,0075 *1021 0,00024 *1019 -0,77 *1021 -0,511 *1021 -0,006 *1021 -0,0001 *1021 0,0002*1019 0,00005*1019 Predominate gravity force Predominate centrifugal force Fg>Fc

From table 2 it is visible, that at 4 planets nearest to the Sun (Mercury, Venus, Earth, Mars), prevails force of gravitation. If to consider not other possible influences on their orbits that they are rotates on decreasing orbits – a descending spiral. From them the fastest decrease at Меркурия, and the slowest at Mars.

Centrifugal force is predominate for the planets Jupiter, Saturn, Uranus, Neptune. Therefore, their orbits are ascending, it is a rising spiral. Of them Jupiter is removed most quickly, and Neptune - slower all.

Orbit asteroid belt - Ceres is descending and among them the most stable. It is a section between ascending and descending orbits. From 4 giant planets the Neptune has most stable orbit. It also is section between descending and ascending orbits. In front of Neptune centrifugal force prevails, but behind it the gravity force is predominate. The orbit of Pluto and Haumea are descending and the most stable of all.

Similar processes are going at numerous satellites of gas planets. Nearest of them have descending orbits, but remote have ascending orbits.

Let's calculate, what would be an orbit of the Earth, if gravity force would be equaled to centrifugal force: 35,404*1021n.

R=√ (G*m1*m2/Fс)

R=√ (6.67384*10-11*1.9891*1030*5.97219*1024/35.404*1021)=1.49643*1011m,

The difference between actual and calculated orbit is 0.00045*1011m or 45000km (it is ~3.5 diameters of the Earth). Consequently, the predominance of a gravity force on 0,021*1021n in comparison with that, which should be at the real speed 2,978*104m/s, gives decrease in an orbit on 45000km, Such difference in radiuses shortens length of an orbit on 2π(R2-R1) ~282600km.

Let's calculate, what would be speed of the Earth, if centrifugal force would be equal to gravity force 35,425n.

v= (F*R/m),

V= (35,425*1021*1.49598*1011/5.97219*1024) 2.9789*104m/s.

Difference between actual and calculated speed is: 2.9789*104-2,978*104= 0.0009*104m/s. That is speed of the Earth on ~9 meters a second is less, than should be at a stable orbit.

On the basis of the premise that dynamics changes of orbits was such a long time, and "scroll" the time ago, we receive, that all the basic planets SS (except  Koiper belt) initially were more close to the asteroid belt and to each other. Decrease of orbits of planets of Koiper belt, probably, occurs only lately.

Influence of mass of space bodies on a ratio of forces

The insignificant increase in mass of planets can occur owing to falling on them of various space bodies: meteorites, asteroids, space dust and other. Changeof mass of planets equally influences to both forces and doesn't break their ratio. The mass of planets can be considered rather invariable, that can't be told about a star. Perhaps, planets can lose mass, for example, owing to burning out of a kernel?

Change the Sun's mass doesn't influence to centrifugal force, but changes gravity. The Sun, burning down, loses about 4.26 million tons/sec or 1.34*1014 tons/year [Wikipedia]. Process of combustion and decrease of mass goes not only on the Sun, but also on other stars. Now the age of SS is about 4.6 billion years. It was determined by the fallen meteorites. Though what guarantee is, that they belong to SS and were formed along with it?! As, other data on age of SS are absent, the mass of the Sun 5 billion years ago, perhaps, was about 1.98977*1027 tons, taking into account decrease coefficient. For all this time the Sun lost 6.7*1023tons, that is approximately equal to two mass of Mercury, it is a little. Perhaps, there is a hidden mass (disintegration), which the Sun loses much quicker?

This factor has to have the constraining impact on the descending orbits and, on the contrary, the accelerating influence on the ascending orbits. The age of SS and speed decrease of mass of the Sun raise big doubts. Most likely, the age of the Sun and speed of decrease of mass much more. Possible, when SS was young, all planets were compactly, near a belt of asteroids. Mass of a Sun was sufficient, that terms for life could be on the farthest planets. Maybe, planets were nearer to each other, and life could exist on a few nearby planets.

The distance from the Sun can be divided into 3 zones conditionally:

1-st, close to the Sun, may call conditionally "red zone", where high temperatures;

2-nd, average, may call conditionally "green zone", where from -50o to +50oC, it is a zone of life;

3-d, distant, may call conditionally "blue zone", where very low temperatures.

On Mars there are pyramids, therefore earlier there was warmer and there were conditions for life and construction. If to assume that initially "zone of life" was behind a belt of asteroids, planets behind a belt of asteroids could pass through "zone of life" in process of untwisting of their orbits. If to assume that at the beginning the Solar energy was enough for life on gas planets, Earth at that time was in "red" - a hot zone. It is known that in the most ancient times the climate was warmer, then gradually was cooling down, and poles of Earth became covered by glaciers.

How it can be explained, if descending of orbit follows from calculation and there has to be a warming of climate? It is possible to assume 2 explanations for it. First assumption: in the period of "the young Sun" all orbit of planets had removing, and only lately orbits of the nearest planets began to decrease (for example, because of aging of the Sun).If to assume that orbits of planets: Mars, Earth, Venus and Mercury, in the period of the young Sun, were stabler and descending slightly, and "zone of life" decreased quicker than their orbits, these can explain passing of Mars through "zone of life". Other explanation: decrease of mass of the Sun goes quicker, than decrease in orbits of planets and it conducts to their cooling. The second, in my opinion, is more possibly.

Cvetlana Denisova

21.01.2014